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A comment on Negative Base. Parent comment

Re:Negative Base by phamilton on Thursday June 28, 2018 @10:48AM (#17417271)
Nope. It's ternary in nature. The subproblem of "You have 3 coins, one of which is lighter than the others. On a balanced scale, figure out which one is lighter in one weighing." is a good place to start. Just enumerate all 3 possible weighings and you should be able to see the correct approach.
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Re:Negative Base by emilfihlman on Thursday June 28, 2018 @04:24PM (#17420178)
How do you solve this?

ABC, one of them is different weight than the other two (either more or less)

Possible ways to weigh them:

  A v B
  A not enough information
  E C is odd one out
  B not enough information

  A v C
  A not enough information
  E B is odd one out
  C not enough information

  B v C
  B not enough information
  E A is odd one out
  C not enough information

  AB v C
  AB not enough information
  E C is odd one out
  C C is odd one out

  AC v B
  AC not enough information
  E B is odd one out
  B B is odd one out

  BC v A
  BC not enough information
  E A is odd one out
  A A is odd one out
In all possible ways to weight 3 coins, all have uncertainty which means you cannot deduce which is the odd one out.
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Re:Negative Base by scrooched_moose on Thursday June 28, 2018 @05:05PM (#17420483)
Your OP stated one is lighter, not one is different.

It's easier than the 12-coin one different puzzle, but introduces the ternary concept well enough to get you started on the harder problem (there are some other complications to it as well).

Weigh 2 coins. If the scales move you've found the lighter coin. If the scales balance, it's the third coin you didn't weigh.

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Re:Negative Base by emilfihlman on Thursday June 28, 2018 @06:05PM (#17420869)
Ah I got the original (12 coins, one is lighter or heavier) mixed up with 3 coins (one is lighter).
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Re:Negative Base by grive on Thursday June 28, 2018 @05:24PM (#17420603)
Label each coin, divide in three stacks each time, and shuffle meaningfully each time the subsets, to remove uncertainty.
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